The invention relates to a method and apparatus for minimizing near end cross talk due to discrete multi-tone (DMT) transmission in cable binders.
In digital communication systems employing multi-channel or multi-carrier transmission, the most effective allocation of bits to the channels has been discussed in the literature. The well-known solution from information theory, analogized to pouring water over a terrain defined by the noise/attenuation of the channel transform characteristic, has been found to insure efficient use of signal power within limits defined by aggregate power and power spectral density mask limits. However, the method in some instances may not go as far as possible in exploiting available power imposed by these limits.
For heuristic purposes, the prior art and the invention are discussed in terms of N quadrature amplitude modulation (QAM) channels with a uniform symbol rate and a non-uniform (unique to each channel) QAM constellation. QAM, a form of combined amplitude and phase modulation, represents k-bit sets of data by modulating two (orthogonal) quadrature carriers, cos 2xcfx80fct and sin 2xcfx80fct to generate a pulse whose phase and amplitude convey the encoded k-bits of information. The QAM signal tone can be and amplitude convey the encoded k-bits of information. The QAM signal tone can be viewed as a phasor in the complex plane, each distinguishable phasor representing a unique state of the tone identified with one unique value in a range. Thus, if the channel and signal power are such that 4 separate phasors can be reliably distinguished, the scheme allows two bits to be represented. For 3 bits to be represented, 8 phasors must be distinguished and so on. The number of different phasors or states that are distinguishable in a single tone (pulse), the QAM constellation, is limited by the signal to noise ratio of the channel and limits imposed by external standards as discussed below.
In a DMT modem, a transmission frequency band is separated into N sub-bands or frequency bins, each corresponding to one QAM channel. In a non-ideal channel each sub-band has a different capacity as a result of the variation of noise and attenuation with frequency. In addition, external standards impose limits on the aggregate power of a signal (the power applied in all sub-band channels) and a cap on the power as a function of frequency defined by a power spectral density mask.
The power spectral density mask may be dictated by a standard used in a particular country implementing the standard (such as A.N.S.I. standard T1.413-1995). The mask may also be a design constraint intentionally imposed by a modem designer for some other reason. For example, a designer may intentionally impose a constraint that no more than n bits are to be transmitted on a transmit channel frequency. Similarly, the designer may impose a constraint that a minimum of bits (or no bits) must be transmitted on a particular tone or frequency. For example, the power limit for frequencies or tones between 0 and 200 kilohertz must be less than xe2x88x9240 dBm/Hz (a power level referenced to one milliwatt over 1 Hz bandwidth). Above 200 kHz (to frequencies, for example, in the megahertz of spectrum), the constraint may be xe2x88x9234 dBm/Hz.
Referring to FIG. 1, the attenuation/noise characteristics of a medium can be graphically represented by a floor in a power spectral graph where frequency may be represented in 100 kHz increments. The lower curve, the channel transform characteristic A, represents this floor, that is, the combined effect of noise and attenuation as a function of frequency. A certain margin of transmit power is required to meet or exceed the minimum threshold of a signal for reliable data transmission. In other words, the power of a signal in a given sub-band must be sufficiently high to carry a minimal (1-bit) QAM tone to obtain a predefined bit error rate. The minimum margin, that is required to transmit a single bit, is represented by curve B. Curve C represents the limits imposed by a power spectral density mask imposed by an external communications standard. The other limit is on the aggregate power, also defined by an external communication standard; for example, ANSI Standard T1.413-1995 limits the total or aggregate power for all sub-bands to 100 m Watts in the downstream direction. Some coding techniques, such as Wei code described in American National Standard for Telecommunicationsxe2x80x94Network and Customer Installation Interfacesxe2x80x94Asymmetric Digital Subscriber Line Metallic Interface, ANSI T1.413-1995, may also require a minimum number of bits in a frequency band if the band is to convey any information at all. In other words, the power spectral density mask limit may require that less energy be used than the minimum required to transmit a single bit.
Note that the minimum allowable size of the power margin is, in part, arbitrary, since, to an extent, it is defined in terms of some a priori rules and technical criteria (which are arbitrary to the extent that they establish a dividing line between acceptable and unacceptable error rates; Bit Error Rate or BER) for the given communication system. Note also that the size of the margin available for a given sub-band corresponds to the dimension of the constellation that can be represented in a signal carried in that QAM channel. That is, the larger the margin in a band, the greater the number of states that can be reliably distinguished in that band and the larger the constellation that can be used.
The above context creates a bit-allocation problem. That is, given the constraints, how should bits be allocated among the available QAM channels to provide the highest possible data rates? DSL modems that use DMT modulation concentrate the transmitted information in the frequency sub-bands that have the minimum attenuation and noise. The optimum distribution of transmission power is obtained by distributing the power according to the well-known xe2x80x9cwater pouringxe2x80x9d analogy as described in Robert C. Gallagher, Information Theory and Reliable Communication, John Wiley and Sons, New York, 1968. Such optimal distribution requires a strategy for allocating bits to the sub-bands for the idealized situation where the channel sub-bands approach zero width. For discrete bits, the applicable metaphor could be described as an ice-cube pouring analogy.
Digital Subscriber loop (DSL) technology was conceived to maximize the throughput on twisted pair copper wiring with attendant background noise, time-variant Far End Cross Talk (FEXT) and Near End Cross Talk (NEXT). To determine the transform characteristic of the channel, the modems at a telecommunications central office and a remote terminal negotiate during an initial channel signal-to-noise ratio (SNR) estimation procedure. During the procedure, the transmitter sends a known pseudo noise (PN) signal. The receiver computes the characteristics of the received signal in the form of a ratio Nk/gk, where gk is the channel gain (inverse of the attenuation) in frequency band k and Nk is the noise power in the band k. The literature contains many algorithms for determining the power distribution across the full frequency bandwidth for maximum data throughput. As noted above, the optimum approach for a non-uniform Gaussian noise channel divided such that each band can be considered an additive white Gaussian noise channel has been proved to be the xe2x80x9cwater pouringxe2x80x9d algorithm of power distribution. In this case, the gk/Nk profile is compared to a terrain and the available aggregate power limit to a fixed supply of water poured over the terrain. The depth of the water corresponds to the power spectral density. The water pouring analogy is inappropriate to allocation of power in digital channels intended for transmission of binary data (bits).
The Digital Subscriber Loop (DSL) modems that use the Discrete Multi-Tone (DMT) technology must use an algorithm for assigning data bits to the multiple tones that are used for modulation. Some algorithms exist in the literature that are designed to optimally allocate the data bits and the budgeted power to the multiple tones. Most of these algorithms are based on the xe2x80x98water-fillingxe2x80x99 approach that postulates that optimal power allocation is obtained when the noise to attenuation ratio is considered as the xe2x80x98terrainxe2x80x99 and the available power is treated as xe2x80x98waterxe2x80x99 to be poured on the terrain. All these algorithms utilize various performance functions that minimize the total allocated power, or maximize the data rate, or a combination of the two. The algorithms are designed with the purpose of either maximizing the total transmitted data rate or meeting the desired data rate, within the constraints of the budgeted total power. This strategy is quite appropriate when the required data rate is such that the DSL transmission loop is power limited. In other words, the bit and power allocation algorithm must perform the allocation such that the maximum number of data bits per frame is allocated to the frequency bins that require the least amount of power for achieving the desired bit error rate (BER).
However, not all cases are power limited. When the required data rate is less than the maximum rate that can be supported on the loop, the assignment of data bits to frequency bins will depend upon the minimization strategy used by the allocation algorithm. The conventional algorithms minimize the total power used for transmitting a given number of data bits in one DMT frame such that the receiver experiences an average BER that is equal to the desired BER. The primary problem at the central office (CO) is that of higher near end cross talk (NEXT) and the algorithms that minimize power may not necessarily minimize the NEXT at the CO, even though the NEXT is proportional to the transmit power.
It is an object of the invention to provide a method and apparatus for allowing any bit/power allocation algorithm to meet the objective of minimizing the near end cross talk at the central office.
The algorithms in the prior art do not specifically attempt to minimize the near end cross talk at the central office, although the implicit intentions of the algorithm designers include the objective of minimizing the NEXT. All other algorithm designers have assumed that since the NEXT is linearly proportional to the transmitted power, minimizing the transmit power is sufficient to minimizing the cross-talk. However, the coupling of the transmit power in a typical cable binder of pairs of twisted copper wires from a source pair to a disturber pair within the binder is a non-linear function of frequency. Therefore, equal power values in two different frequency bins result in different levels of cross-talk power. The invention solves this problem by altering the performance function that is used by the conventional algorithms.